Excerpt from Reflection and Transmission of Electromagnetic Waves by Thin Curved Shells

In order to solve the prohlen it is necessary to obtain, in the oh stacle as well as in the surrounding medium, a solution of Maxwell's equations which satisfies the boundary conditions on the obstacle boundary. This solution must also contain the incident field. For incident plane or spherical waves this last condition can be fulfilled. By requiring the solution to have an appropriate singularity at the source, in other cases this condition may be more troublesome.

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